Help me with some basic physics?

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Hello. I am trying to get my head around free body force diagrams and have not done this for ages, so wonder if someone could offer some guidance:

Let us suppose that a horse is pulling a plough through a field. A certain amount of friction is present between the plough and the ground, and this had to be overcome before the plough started to move. The plough starts moving, due to a resultant force in the direction of movement - leading to an acceleration from F = m x a.

So far so good (I think). Now, let us say that the horse keeps applying a steady force once the speed of the plough has reached 1 m/s. There is no further acceleration, so now there is no longer a resultant force. So where did the excess force 'go'? I can only identify the constant friction opposing the applied force, but there must be something else in there which is preventing the plough from accelerating further!

For the sake of simplicity, I have not included factors such as the weight of the plough (although presumably that dictates the amount of friction) or wind resistance on the horse/plough. Just trying to consider the horizontal forces.

I'm thinking that some other force in the opposite direction is increasing as the plough accelerates, and then once this force (plus the kinetic friction) equals the force being applied by the horse, the plough just continues at a constant velocity. But what is the force!?

Thanks.
 
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It is just the friction - when a body is moving through a medium, the drag (frictional forces acting on the plough) increases in proportion to velocity squared. (double the velocity = 4x drag)

The plough through the ground can be considered the same as this - At 1m/s you'd assume the drag has equal magnetude to the force being applied by the horse, so the acceration tends to 0.
This drag will be a combination of form drag (that caused by the cross section moving into the soil) and the skin drag (the resistance of the soil moving agaist the plough's sides)

Other factors to consider are the friction changes from static, to dynamic (the object is easier to move once it has started moving), also the horse could be considered to stop pulling as hard once it has reached a certain speed so the acceleration will stop.
 
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